One of our main activities over the last few years has been the development of a comprehensive model for oscillations of membrane potential and calcium on time scales ranging from seconds to minutes. These lead to corresponding oscillations of insulin secretion. The basic hypothesis of the model is that the faster oscillations (tens of seconds) stem from feedback of calcium onto ion channels, likely calcium-activated potassium (K(Ca)) channels and ATP-dependent potassium (K(ATP)) channels, whereas the slower oscillations (five minutes) stem from oscillations in metabolism. The metabolic oscillations are transduced into electrical oscillations via the K(ATP) channels. The model thus consists of an electrical oscillator (EO) and a metabolic oscillator (MO) and is referred to as the Dual Oscillator Model (DOM). In our model, the MO is a glycolytic oscillator, but many of the features of the system would still hold if the metabolic oscillation arose elsewhere, such as the mitochondria. K(ATP) channels are of clinical significance as they are a first-line target of insulin-stimulating drugs, such as the sulfonylureas tolbutamide and glyburide, used in the treatment of Type 2 Diabetes. Severe gain-of-function mutations of K(ATP) are a major cause of neo-natal diabetes mellitus, whereas moderate gain-of-function mutations have been linked in genome-wide association studies (GWAS) to the milder but more common disease, adult-onset type 2 diabetes. Conversely, loss-of-function mutations of K(ATP) are a major cause of familial hyperinsulinism, a hereditary disease found in children in which beta cells are persistently electrically active and secrete insulin in the face of normal or low glucose, causing life-threatening hypoglycemia. The key element in our model for glycolytic oscillations is the positive feedback on the activity of phosphofructokinase-1 (PFK1) by its product fructose-1,6-bisphosphate (Fru1,6-BP). However, a related enzyme, phosphofructokinase-2 (PFK2) produces fructose-2,6-bisphosphate (Fru2,6-BP), which activates PFK1 even more strongly than Fru1,6-BP. PFK2 is a particularly interesting molecule in that it is part of a bifunctional enzyme (BIF2) that contains both the kinase and its corresponding phosphatase, fructose-2,6-bisphosphatase (FBPase2). Our collaborators in the Satin lab (University of Michigan) used a novel technique to overexpress either PFK2 or FBPase2 or BIF2 with either kinase-dead or phosphatase-dead moieties. We found that increasing the activity of the kinase relative to the phosphatase increases the frequency and reduces the amplitude of slow calcium oscillations whereas increasing the relative activity of the phosphatase had the opposite effect. Simulations and analysis of the model showed that increased Fru2,6-BP increases frequency by lowering the threshold for PFK1 activation by its substrate, fructrose-6-phosphate. PFK2, however, is not able to drive oscillations by itself since it does not receive positive feedback from its product. The agreement of the experimental observations with the predictions of the DOM lends further support to the model, in particular supporting the hypothesis that the metabolic oscillations originate in glycolysis rather than, say, the mitochondria; it is difficult to see how a specific modification of glycolysis would have the observed effects on a mitochondrial oscillator. This work is described in Ref. # 1. On a more theoretical level, we have made important progress in our long-term goal of classifying bursting oscillations found in a variety of cell types and relating the beta-cell variety to other forms. This is described in detail in our project report on Mathematical Modeling of Neurons and Endocrine Cells. Other studies in progress include measurements and simulations of K(ATP) channel conductance oscillations, modeling the effect of knocking out the ion channel Trpm5 to selectively suppress fast electrical oscillations, and extending the DOM to pancreatic alpha cells that secrete glucagon.